Problem: Simplify the following expression: $ x = \dfrac{z - 3}{-5} + \dfrac{-8}{9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{z - 3}{-5} \times \dfrac{9}{9} = \dfrac{9z - 27}{-45} $ Multiply the second expression by $\dfrac{-5}{-5}$ $ \dfrac{-8}{9} \times \dfrac{-5}{-5} = \dfrac{40}{-45} $ Therefore $ x = \dfrac{9z - 27}{-45} + \dfrac{40}{-45} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{9z - 27 + 40}{-45} $ $x = \dfrac{9z + 13}{-45}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{-9z - 13}{45}$